Question

On July 1, 2013 an investment manager purchased five-hundred $1,000 par value bonds with an 8.75% coupon rate for $467,000. The bonds mature on July 15, 2021. a. According to this information, would you expect that the rates being offered by similar investments on the open market carry a rate that is higher, or lower, than the coupon rate? Explain. b. Find the current yield AND the yield to maturity. Show your work.

Answer 1

a. Par value of the bond is $ 1000

And its current market price = total purchase price/ number of bonds = $467,000/500 = $934

As the current market price of the bond is less than its par value, therefore we can expect that rates being offered by similar investments on the open market carry a rate that is higher than the coupon rate.

b. Bond’s current yield

Current yield = annual coupon payment / market price of bond

Where,

Annual coupon payment = 8.75% of $1000 = $87.50

Market price of bond = $934

Therefore,

Current yield = $87.50 / $934 = 0.0937 or 9.37%

Now we have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

M = value at maturity, or par value = $ 1000

P0 = the current market price of bond = $934

C = coupon payment = 8.75% of $1000 = $87.50

n = number of payments (time remaining to maturity) = 8 years 15 days or 8+ 15/365 = 8.041 years (purchased on July 1, 2013 and mature on July 15, 2021)

YTM = interest rate, or yield to maturity =?

Now we have,

$934 = $87.50 * [1 – 1 / (1+YTM) ^8.041] /YTM+ 1000 / (1+YTM) ^8.041

By trial and error method we can calculate the value of YTM = 9.98%

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(8.41,-87.50,934,-1000)” = 9.98%]

Therefore YTM is 9.98% which is more than the coupon rate